Population data
2, 4, 4, 4, 5, 5, 7, 9Population SD = 2
Standard Deviation Calculator
Use this free standard deviation calculator to find sample standard deviation, population standard deviation, variance, mean, count, steps, copy, and history.
Inputs to check Example numbers Copyable answer Tab-only history
Sample standard deviation2.1380899353
- Mean
- 5
- Variance
- 4.5714285714
- Count
- 8
Steps
- Find the mean: 5.
- Find each distance from the mean and square it.
- Divide by n - 1 for sample variance.
- Take the square root of the variance.
How to use the Standard Deviation Calculator
- Enter a list of numbers separated by commas, spaces, or line breaks.
- Choose Sample when your values are a sample, or Population when the list is the full group.
- Press Calculate standard deviation to see variance, mean, range, and formula steps.
- Use examples, recent answers, or copy the result while checking statistics work.
What people use it for
Measure how spread out a list of numbers is from its mean.
Compare sample standard deviation with population standard deviation.
Check statistics homework, study data, measurements, and class examples.
Copy the standard deviation, variance, mean, and count for notes.
Quick examples
Sample data
2, 4, 4, 4, 5, 5, 7, 9Sample SD = 2.1380899353
Small data set
12, 15, 19, 21, 22, 26Mean = 19.1666666667
Need the guide or a nearby tool?
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- How to use the Standard Deviation Calculator See slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
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Frequently asked questions
Quick answers about formulas, inputs, examples, result copying, and private in-browser history.
What does standard deviation measure?
Standard deviation measures how far data values typically are from the mean. A larger standard deviation means the values are more spread out.
Should I use sample or population standard deviation?
Use sample standard deviation when your data is a sample that estimates a larger population. Use population standard deviation when the data includes the whole group you care about.
What do the main Standard Deviation Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Standard Deviation Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Standard Deviation Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
Why does sample standard deviation divide by n - 1?
Sample standard deviation divides by n - 1 to correct for estimating population spread from a sample. This is often called Bessel correction.
How many values can I enter?
You can enter up to 1,000 values separated by commas, spaces, semicolons, or new lines.
Can the standard deviation be zero?
Yes. Standard deviation is zero when every value in the data set is exactly the same.
Is my standard deviation history private?
Yes. Recent answers stay only in the current browser tab while you use the page. They are not sent to a server.
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